The $B^0$, $B^0_s$, $B^+$ and $Lambda^0_b$ hadron production asymmetries are measured using a data sample corresponding to an integrated luminosity of 3.0 fb$^{-1}$, collected by the LHCb experiment in proton-proton collisions at centre-of-mass energies of 7 and 8 TeV. The measurements are performed as a function of transverse momentum and rapidity of the $b$ hadrons within the LHCb detector acceptance. The overall production asymmetries, integrated over transverse momentum and rapidity, are also determined.